We consider a dynamical system generated by an analytic perturbation Aɛ of an analytic Anosov diffeomorphism A0 of T d . We show that, if A0 admits a splitting of T T d in k invariant subspaces, there exists a partial conjugation H ϵ of dAɛ and dA0 that preserves the splitting and is analytic in ɛ. This shows that the splitting can be extended to Aɛ. As an application of this results, we obtain that the Lyapunov exponents, if non degenerate, are analytic functions of the perturbation.
Marin, G.M., Bonetto, F., Corsi, L. (2025). Analiticity of the Lyapunov exponents of perturbed toral automorphisms. JOURNAL OF MATHEMATICAL PHYSICS, 66(4) [10.1063/5.0183157].
Analiticity of the Lyapunov exponents of perturbed toral automorphisms
Bonetto, Federico;Corsi, Livia
2025-01-01
Abstract
We consider a dynamical system generated by an analytic perturbation Aɛ of an analytic Anosov diffeomorphism A0 of T d . We show that, if A0 admits a splitting of T T d in k invariant subspaces, there exists a partial conjugation H ϵ of dAɛ and dA0 that preserves the splitting and is analytic in ɛ. This shows that the splitting can be extended to Aɛ. As an application of this results, we obtain that the Lyapunov exponents, if non degenerate, are analytic functions of the perturbation.| File | Dimensione | Formato | |
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